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On modular forms and the inverse Galois problem
Dieulefait, L. V. (Luis Victor); Wiese, Gabor
Universitat de Barcelona
In this article new cases of the inverse Galois problem are established. The main result is that for a fixed integer $ n$, there is a positive density set of primes $ p$ such that $ \mathrm{PSL}_2(\mathbb{F}_{p^n})$ occurs as the Galois group of some finite extension of the rational numbers. These groups are obtained as projective images of residual modular Galois representations. Moreover, families of modular forms are constructed such that the images of all their residual Galois representations are as large as a priori possible. Both results essentially use Khare's and Wintenberger's notion of good-dihedral primes. Particular care is taken in order to exclude nontrivial inner twists.
Grups discontinus
Formes automòrfiques
Teoria de nombres
Discontinuous groups
Automorphic forms
Number theory
(c) American Mathematical Society (AMS), 2011
American Mathematical Society (AMS)

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